Argumentation semantics based on solid admissibility and preservation of semantic properties

This paper proposes novel semantics based on solid admissibility, which strengthens Dung’s admissibility by incorporating a condition that an argument requires all defenders for it to be successfully defended. These solid semantics provide a better approach to handling controversial scenarios in Dung’s argumentation framework compared to Dung’s semantics. Specifically, if two arguments are such that one of them indirectly attacks a third argument while the other one indirectly defends the third one, then the three arguments cannot be included in the same solid extension. Furthermore, an argument that is indirectly attacked and indirectly defended by another argument (controversial arguments) cannot be an element of any solid extension. Additionally, applying solid semantics to judgment aggregation yields more positive aggregation outcomes than Dung’s semantics; notably, any quota rule higher than or equal to the strict majority rule preserves solid admissibility for all argumentation frameworks but fails to preserve Dung’s admissibility.